# Polynomial Regression – Advice Needed

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Viewing 13 posts - 1 through 13 (of 13 total)
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• #55735

Gustav
Participant

Six Sigma Green Belt here, Im trying to develop some kind of statistical model that lets me estimate sales by the end of the month based off of my sales at any given point of time during the month. Ive noticed that sales trend on a polynomial curve consistently increasing rapidly as I move towards the end of the month.

I’ve mapped 4 years of daily sales data against business day of the month to get a sales curve. Ive then plotted a polynomial regression line over my data and used excel solver on the coefficients to get a line with an R squared of .997. Pretty good line.

However, I now realize that all I can do with my equation is predict sales based off of a day or predict working day based off of sales. It does not let me predict sales at the end of the month based of off my sales number at a point in time. I can get an approximation by taking my % increase for a historical point in time to my line apex, but I feel like there are more scientific ways of going about this.

Any advice on any techniques I can employ to achieve my goal?

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#201421

MBBinWI
Participant

@TollemG – maybe concentrate more on selling instead of trying to predict sales?

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#201422

John Noguera
Participant

Use Excel 2016 Forecast.ETS (easiest) or Minitab’s Exponential Smoothing or ARIMA.

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#201423

Gustav
Participant

Minitab’s Exponential Smoothing

Thank you sir, this worked perfectly, should have a significant impact on my weekly forecast accuracy.

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#201424

Gustav
Participant

@MBBinWI cant sell if we don’t have lead time to set appropriate production schedules to fill demand. Also selling is not my job.

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#201425

John Noguera
Participant

You are welcome. Be sure to check the autocorrelation (ACF) plot on the residuals to ensure that the model is adequate.

Also same assumptions as in a Regression model: residuals should be approximately normal and have equal variance.

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#201426

John Noguera
Participant

Forgot to mention the Ljung-Box test on the residuals is a good complement to the ACF plot.

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#201427

Robert Butler
Participant

The smoothing and/or ARIMA may or may not have a significant impact on your ability to make accurate weekly forcasts. In addition to the basic trend line you also need to plot your 95% CI and watch what happens once you are in the realm of forecasting.

The terms in your model might be adequate and thus your prediction limits may be such that the prediction and the error associated with the prediction are good enough to provide some degree of confidence in the forecast. On the other hand, the error associated with the predictions could be so high as to reduce the entire effort to nothing more than expensive science fiction.

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#201428

John Noguera
Participant

https://robjhyndman.com/hyndsight/show-me-the-evidence/

Using thousands of data sets from the M3 forecast competition, he shows that the compound hybrid of Exponential Smoothing and ARIMA outperform all commercial forecast tools. Of course “all models are wrong, some are useful” but this is an interesting approach to more useful models!

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#201446

Gustav
Participant

@jnoguera How does exponential smoothing treat seasonality when there are different time intervals to the seasonality. It seems that I have to designate a seasonality cycle for the model to work over time, however, since my cycle is not always the same amount of business days

What I mean by this is that my “seasonality” is really just a big uptick in sales open orders in the last ~3-5 business days of the month. However, when adjusted for holidays and weekends some months will have 20 business days, some will have 19, some will have 21. Is there any way for my ETS model to account for this? I face the same problem when I try to use seasonality coefficients on working days.

The only real solution I have come up with is to run a separate ETS model on each month since people generally get a day off even if a moving holiday falls on a weekend.

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#201447

John Noguera
Participant

De Livera and Hyndman developed a model for complex seasonality called TBATS:

https://robjhyndman.com/papers/ComplexSeasonality.pdf

Unfortunately (for now) this is only available in R, so I suggest:

Install Base R
Install R Studio
Install the forecast package.

I hope that helps. Let me know if that works for you.

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#201448

Gustav
Participant

@jnoguera Doesn’t look simple, but there’s no time like the present to learn something new. Thank you for your help, will report back with my success hopefully sooner rather than later.

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#201449

John Noguera
Participant

I agree – this is not simple, but the hard part will be getting familiar with the basics of the R language, and getting the data in (which is why I suggested R Studio).

P.S. If you are successful with TBATS, that will have an impact on our DiscoverSim development plans – p.m. me for details.

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